Stringy Chow Rings and Weighted Blow-Ups

Abstract We compute the stringy Chow ring of a general Deligne–Mumford stack of the form $[X/G]$ for a smooth variety $X$ and diagonalizable group scheme $G$, working over a base field that is not necessarily algebraically closed. We then specialize to the stringy Chow ring of the weighted blow-up of a smooth variety along a smooth center. We explore finite generation properties of this ring.